Problem: In the right triangle shown, $AC = 3$ and $AB = 6$. What is $BC$ ? $A$ $C$ $B$ $3$ $?$ $6$
Answer: We know $a^2 + b^2 = c^2$ We want to find $a$ ; let $b = 3$ and $c = 6$ So $a^2 = c^2 - b^2 = 6^2 - 3^2 = 27$ Then, $a = \sqrt{27}$ Simplifying the radical gives $a = 3\sqrt{3}.$